Bo'linuvchanlik. Sonning natural bo'luvchilar soni va yig'indisi bo‘yicha savol

56 sonining tub ko‘paytuvchilari $2^{3}\cdot7$ ga teng. Agar $n=p_{1}^{a_{1}}p_{2}^{a_{2}}\dots p_{k}^{a_{k}}$ bo‘lsa, uning barcha natural bo‘luvchilar yig‘indisi $\displaystyle \prod_{i=1}^{k}\frac{p_{i}^{\,a_{i}+1}-1}{p_{i}-1}$ formulasi bilan hisoblanadi. Demak, \[ \text{yig‘indi}= \frac{2^{3+1}-1}{2-1}\cdot\frac{7^{1+1}-1}{7-1} = \frac{2^{4}-1}{1}\cdot\frac{7^{2}-1}{6} = (16-1)\cdot\frac{49-1}{6} = 15\cdot 8 =120. \] Shu sababli 56 sonining natural bo‘luvchilar yig‘indisi **120** ga teng.